A solid concrete wall has dimensions 4.0 m x 2.4 m and is 30 cm thick. The thermal conductivity of the concrete is $1.3 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$ and it separates a basement from the ground outside. The inner surface of the wall is at $18 ^ { \circ } \mathrm { C }$ and the outside surface is at $6 ^ { \circ } \mathrm { C }$ How much heat flows through the wall every hour?

Question

A solid concrete wall has dimensions  4.0 m x 2.4 m and is  30 cm thick. The thermal conductivity of the concrete is $1.3 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$ and it separates a basement from the ground outside. The inner surface of the wall is at $18 ^ { \circ } \mathrm { C }$ and the outside surface is at $6 ^ { \circ } \mathrm { C }$ How much heat flows through the wall every hour?

Quizplus · Accepted Answer

The heat flow through the wall can be calculated using the formula $Q = \frac{k \cdot A \cdot \Delta T \cdot t}{d}$, where $Q$ is the heat flow, $k$ is the thermal conductivity, $A$ is the area of the wall, $\Delta T$ is the temperature difference across the wall, $t$ is the time, and $d$ is the thickness of the wall. Plugging in the given values: $Q = \frac{1.3 \cdot (4.0 \cdot 2.4) \cdot (18 - 6) \cdot 3600}{0.3}$, we find that $Q = 1,814,400 \, \text{J}$ or $1.8 \, \text{MJ}$.

A Solid Concrete Wall Has Dimensions 4 1.3 W/m⋅K1.3 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }1.3 W/m⋅K

A Solid Concrete Wall Has Dimensions 4 $1.3 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$